Make sure you're using the latest Optifine too. (C3)

That issue is likely caused by the pack being too much for your PC to handle. Try a lower resolution or go without the addon.

Animated textures only affect FPS, not atlas size. As @MauveCloud said, the first frame of the animation is put in the atlas, then the other frames are rendered in real time. As for choosing which textures should be animated, the Customiser can be used to switch animated textures to their static alt...

That may be, but 16384^2 is a good baseline to work for. Only a minority will be capable of higher, and if their gpu can't take it, there are plenty of lower resolutions.

Sure :) Basically, Minecraft generates a massive texture sheet, of all the textures stitched together. Due to hardware limitations, the maximum size this atlas can be is 16384*16384. If your textures, when stitched, exceed this limit, Minecraft will crash. Currently 512x is on the verge of exceeding...

But if you read my edit, I was informed that due to some weird programming by the dev of EU, that method does not work.

I'm not sure what you mean. ExtraUtils doesn't like netherrack being an animation, thus you need to use the static image, located in blocks_alt_static.

Ah, that'd be it. According to https://github.com/rwtema/extrautilities/issues/862#issuecomment-230111590, ExtraUtils has an issue with the netherrack being an animation. Try using https://hanfox.co.uk/bdcraft_custom/ and selecting the static netherrack. ;) Edit: I've been informed that this doesn't...

What mods are you using?

Some textures can be found here: https://imgur.com/a/GLVzH So you can put them in the right place if you know what you're doing